论文标题
半线性耗散双曲线PDE的强制频率锁定
Forced Frequency Locking for Semilinear Dissipative Hyperbolic PDEs
论文作者
论文摘要
本文涉及对一维耗散自主半线性双曲线PDE的时间周期性溶液在小时周期强迫的影响下的行为。我们表明，强制频率锁定的现象与以ODE或抛物线PDES闻名的类似现象类似。但是，与ODE或抛物线PDE相比，证明本质上要困难得多。特别是，需要非共振条件，在ODE或抛物线PDE的情况下没有对应条件。我们得出一个标量方程式，该方程回答了强制频率锁定的主要问题：在哪个强迫下，解决方案向未强制方程式的哪个时间变化？
This paper concerns the behavior of time-periodic solutions to 1D dissipative autonomous semilinear hyperbolic PDEs under the influence of small time-periodic forcing. We show that the phenomenon of forced frequency locking happens similarly to the analogous phenomena known for ODEs or parabolic PDEs. However, the proofs are essentially more difficult than for ODEs or parabolic PDEs. In particular, non-resonance conditions are needed, which do not have counterparts in the cases of ODEs or parabolic PDEs. We derive a scalar equation which answers the main question of forced frequency locking: Which time shifts of the solution to the unforced equation do survive under which forcing?
